Universe, Volume 5, Issue 3 (March 2019) – 20 articles

This manuscript aims at giving new advances on the functional renormalization group applied to the tensorial group field theory. It is based on the series of our three papers (Lahoche, et al., Class. Quantum Gravity 2018, 35, 19), (Lahoche, et al., Phys. Rev. D 2018, 98, 126010) and (Lahoche, et al., Nucl. Phys. B, 2019, 940, 190–213). We consider the polynomial Abelian $U{\left(1\right)}^d$ models without the closure constraint. More specifically, we discuss the case of the quartic melonic interaction. We present a new approach, namely the effective vertex expansion method, to solve the exact Wetterich flow equation and investigate the resulting flow equations, especially regarding the existence of non-Gaussian fixed points for their connection with phase transitions. To complete this method, we consider a non-trivial constraint arising from the Ward–Takahashi identities and discuss the disappearance of the global non-trivial fixed points taking into account this constraint. Finally, we argue in favor of an alternative scenario involving a first order phase transition into the reduced phase space given by the Ward constraint. Full article

Anti-Newtonian expansions are introduced for scalar quantum field theories and classical gravity. They expand around a limiting theory that evolves only in time while the spatial points are dynamically decoupled. Higher orders of the expansion re-introduce spatial interactions and produce overlapping lightcones from the limiting isolated world line evolution. In scalar quantum field theories, the limiting system consists of copies of a self-interacting quantum mechanical system. In a spatially discretized setting, a nonlinear “graph transform” arises that produces an in principle exact solution of the Functional Renormalization Group for the Legendre effective action. The quantum mechanical input data can be prepared from its $1+0$ dimensional counterpart. In Einstein gravity, the anti-Newtonian limit has no dynamical spatial gradients, yet remains fully diffeomorphism invariant and propagates the original number of degrees of freedom. A canonical transformation (trivialization map) is constructed, in powers of a fractional inverse of Newton’s constant, that maps the ADM action into its anti-Newtonian limit. We outline the prospects of an associated trivializing flow in the quantum theory. Full article

In this paper, we propose that cosmological time is a quantum observable that does not commute with other quantum operators essential for the definition of cosmological states, notably the cosmological constant. This is inspired by properties of a measure of time—the Chern–Simons time—and the fact that in some theories it appears as a conjugate to the cosmological constant, with the two promoted to non-commuting quantum operators. Thus, the Universe may be “delocalised” in time: it does not know the time, a property which opens up new cosmological scenarios, as well as invalidating several paradoxes, such as the timelike tower of turtles associated with an omnipresent time line. Alternatively, a Universe with a sharply defined clock time must have an indeterminate cosmological constant. The challenge then is to explain how islands of localized time may emerge, and give rise to localized histories. In some scenarios, this is achieved by backward transitions in quantum time, cycling the Universe in something akin to a time machine cycle, with classical flow and quantum ebbing. The emergence of matter in a sea of Lambda probably provides the ballast behind classical behaviour. Full article

If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches to quantization, indicate a similar short-distance dimensional reduction. I will review the evidence for this behavior, emphasizing the physical question of what one means by “dimension” in a quantum spacetime, and will discuss possible mechanisms that could explain the universality of this phenomenon. Full article

This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformation of the connection, a rescaling of the orthonormal frame, and a combination of the two. The most general second order quadratic metric-affine action, including the parity-violating terms, is constructed in each of the three cases. The results can be straightforwardly generalised by including higher derivatives, and implemented in the general metric-affine, teleparallel, and symmetric teleparallel geometries. Full article

Revisiting the fast fermion damping rate calculation in a thermalized QED and/or QCD plasma in thermal equilibrium at four-loop order, focus is put on a peculiar perturbative structure which has no equivalent at zero-temperature. Not surprisingly, and in agreement with previous $C^{\star }$ -algebraic analyses, this structure renders the use of thermal perturbation theory more than questionable. Full article

The observer’s frame is the more elementary description of the gravitational field than the metric. The most general covariant, even-parity quadratic form for the frame field in arbitrary dimension generalises the New General Relativity by nine functions of the d’Alembertian operator. The degrees of freedom are clarified by a covariant derivation of the propagator. The consistent and viable models can incorporate an ultra-violet completion of the gravity theory, an additional polarisation of the gravitational wave, and the dynamics of a magnetic scalar potential. Full article

In particular, Riemann’s impact on mathematics and physics alike is demonstrated using methods originating from the theory of numbers and from quantum electrodynamics, i.e., from the behavior of an electron in a prescribed external electromagnetic field. More specifically, we employ Riemann’s zeta function to regularize the otherwise infinite results of the so-called Heisenberg–Euler Lagrangian. As a spin-off, we also calculate some integrals that are useful in mathematics and physics. Full article

Assuming the Multiple Point Principle (MPP) as a new law of Nature, we considered the existence of the two degenerate vacua of the Universe: (a) the first Electroweak (EW) vacuum at $v_1\approx 246$ GeV—“true vacuum”, and (b) the second Planck scale “false vacuum” at $v_2\sim {10}^{18}$ GeV. In these vacua, we investigated different topological defects. The main aim of the paper is an investigation of the black-hole-hedgehogs configurations as defects of the false vacuum. In the framework of the $f\left(R\right)$ gravity, described by the Gravi-Weak unification model, we considered a black-hole solution, which corresponds to a “hedgehog”—global monopole, that has been “swallowed” by the black-hole with mass core $M_{BH}\sim {10}^{18}$ GeV and radius $\delta \sim {10}^{-21}$ GeV ${}^{-1}$ . Considering the results of the hedgehog lattice theory in the framework of the $SU\left(2\right)$ Yang-Mills gauge-invariant theory with hedgehogs in the Wilson loops, we have used the critical value of temperature for the hedgehogs’ confinement phase ( $T_c\sim {10}^{18}$ GeV). This result gave us the possibility to conclude that the SM shows a new physics (with contributions of the $SU\left(2\right)$ -triplet Higgs bosons) at the scale ∼10 TeV. This theory predicts the stability of the EW-vacuum and the accuracy of the MPP. Full article

In attempt to find a proper space of function expressing the eigenvalue of the color-singlet BFKL equation in $N=4$ SYM, we consider an analytic continuation of harmonic sums from positive even integer values of the argument to the complex plane. The resulting meromorphic functions have pole singularities at negative integers. We derive the reflection identities for harmonic sums at weight four decomposing a product of two harmonic sums with mixed pole structure into a linear combination of terms each having a pole at either negative or non-negative values of the argument. The pole decomposition demonstrates how the product of two simpler harmonic sums can build more complicated harmonic sums at higher weight. We list a minimal irreducible set of bilinear reflection identities at weight four, which represents the main result of the paper. We also discuss how other trilinear and quadlinear reflection identities can be constructed from our result with the use of well known quasi-shuffle relations for harmonic sums. Full article

We discuss the particle horizon problem in the framework of spatially homogeneous and isotropic scalar cosmologies. To this purpose we consider a Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime with possibly non-zero spatial sectional curvature (and arbitrary dimension), and assume that the content of the universe is a family of perfect fluids, plus a scalar field that can be a quintessence or a phantom (depending on the sign of the kinetic part in its action functional). We show that the occurrence of a particle horizon is unavoidable if the field is a quintessence, the spatial curvature is non-positive and the usual energy conditions are fulfilled by the perfect fluids. As a partial converse, we present three solvable models where a phantom is present in addition to a perfect fluid, and no particle horizon appears. Full article

We review the study of the scaling properties of geometric operators, such as the geodesic length and the volume of hypersurfaces, in the context of the Asymptotic Safety scenario for quantum gravity. We discuss the use of such operators and how they can be embedded in the effective average action formalism. We report the anomalous dimension of the geometric operators in the Einstein–Hilbert truncation via different approximations by considering simple extensions of previous studies. Full article

We investigate the bounce realization in the framework of generalized modified gravities arising from Finsler and Finsler-like geometries. In particular, a richer intrinsic geometrical structure is reflected in the appearance of extra degrees of freedom in the Friedmann equations that can drive the bounce. We examine various Finsler and Finsler-like constructions. In the cases of general very special relativity, as well as of Finsler-like gravity on the tangent bundle, we show that a bounce cannot easily be obtained. However, in the Finsler–Randers space, induced scalar anisotropy can fulfil bounce conditions, and bouncing solutions are easily obtained. Finally, for the general class of theories that include a nonlinear connection, a new scalar field is induced, leading to a scalar–tensor structure that can easily drive a bounce. These features reveal the capabilities of Finsler and Finsler-like geometries. Full article

Weakly Interacting Massive Particle (WIMP) remains one of the most promising dark matter candidates. Many experiments around the world are searching for WIMPs and the best current sensitivity to WIMP-nucleon spin-independent cross-section is about ${10}^{-10}$ pb. LUX has been one of the world-leading experiments in the search for dark matter WIMPs. Results from the LUX experiment on WIMP searches for different WIMP masses are summarised in this paper. The LUX detector will be replaced by its successor, the LUX-ZEPLIN (LZ) detector. With 50 times larger fiducial mass and an increased background rejection power due to specially-designed veto systems, the LZ experiment (due to take first data in 2020) will achieve a sensitivity to WIMPs exceeding the current best limits by more than an order of magnitude (for spin-independent interactions and for WIMP masses exceeding a few GeV). An overview of the LZ experiment is presented and LZ sensitivity is discussed based on the accurately modelled background and the high-sensitivity material screening campaign. Full article

Precise measurements of the energy spectra and of the composition of cosmic rays in the PeV region could improve our knowledge regarding their origin, acceleration mechanism, propagation, and composition. At the present time, spectral measurements in this region are mainly derived from data collected by ground-based detectors, because of the very low particle rates at these energies. Unfortunately, these results are affected by the high uncertainties typical of indirect measurements, which depend on the complicated modeling of the interaction of the primary particle with the atmosphere. A space experiment dedicated to measurements in this energy region has to achieve a balance between the requirements of lightness and compactness, with that of a large acceptance to cope with the low particle rates. CaloCube is a four-year-old R&D project, approved and financed by the Istituto Nazionale di Fisica Nucleare (INFN) in 2014, aiming to optimize the design of a space-borne calorimeter. The large acceptance needed is obtained by maximizing the number of entrance windows, while thanks to its homogeneity and high segmentation this new detector achieves an excellent energy resolution and an enhanced separation power between hadrons and electrons. In order to optimize detector performances with respect to the total mass of the apparatus, comparative studies on different scintillating materials, different sizes of crystals, and different spacings among them have been performed making use of MonteCarlo simulations. In parallel to simulations studies, several prototypes instrumented with CsI(Tl) (Caesium Iodide, Tallium doped) cubic crystals have been constructed and tested with particle beams. Moreover, the last development of CaloCube, the Tracker-In-Calorimeter (TIC) project, financed by the INFN in 2018, is focused on the feasibility of including several silicon layers at different depths in the calorimeter in order to reconstruct the particle direction. In fact, an important requirement for $\gamma$ -ray astronomy is to have a good angular resolution in order to allow precise identification of astrophysical sources in space. In respect to the traditional approach of using a tracker with passive material in front of the calorimeter, the TIC solution can save a significant amount of mass budget in a space satellite experiment, which can then be exploited to improve the acceptance and the resolution of the calorimeter. In this paper, the status of the project and perspectives for future developments are presented. Full article

The recently proposed holography-inspired approach to quantum gravity is reviewed and expanded. The approach is based on the foliation of the background spacetime and reduction of the offshell states to the physical states. Careful attention is paid to the boundary conditions. It is noted that the outstanding problems such as the cosmological constant problem and black hole information can be tackled from the common thread of the quantized gravity. One-loop renormalization of the coupling constants and the beta function analysis are illustrated. Active galactic nuclei and gravitational waves are discussed as the potential applications of the present quantization scheme to astrophysics. Full article

A list of all possible causal relations in the two-dimensional Minkowski space M is exhausted, based on the duality between timelike and spacelike in this particular case, and thirty topologies are introduced, all of them encapsulating the causal structure of M. Generalisations of these results are discussed, as well as their significance in a discussion on spacetime singularities. Full article

Evolution of directed flow of charged particles produced in relativistic heavy-ion collisions at energies $4\le \sqrt{s}\le 19.6$ GeV is considered within two microscopic transport models, ultra-relativistic quantum molecular dynamics (UrQMD) and quark-gluon string model (QGSM). In both models, the directed flow of protons changes its sign at midrapidity from antiflow to normal flow with decreasing energy of collisions, whereas the flows of mesons and antiprotons remain antiflow-oriented. For lighter colliding systems, such as Cu+Cu or S+S, changing of the proton directed flow occurs at lower bombarding energies and for more central topologies compared to a heavy Au+Au system. The differences can be explained by dissimilar production zones of different hadrons and by the influence of spectators. Directed flows of most abundant hadronic species at midrapidity are found to be formed within t = 10–12 fm/c after the beginning of nuclear collision. The influence of hard and soft mean-field potentials on the directed flow is also studied. Full article

Extensions of Einstein’s General Relativity (GR) can formally be given a GR structure in which additional geometric degrees of freedom are mapped on an effective energy-momentum tensor. The corresponding effective cosmic medium can then be modeled as an imperfect fluid within GR. The imperfect fluid structure allows us to include, on a phenomenological basis, anisotropic stresses and energy fluxes which are considered as potential signatures for deviations from the cosmological standard $\Lambda$ -cold-dark-matter ( $\Lambda$ CDM) model. As an example, we consider the dynamics of a scalar-tensor extension of the standard model, the $e_{\Phi }\Lambda$ CDM model. We constrain the magnitudes of anisotropic pressure and energy flux with the help of redshift-space distortion (RSD) data for the matter growth function $f{\sigma }_8$ . Full article

We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton’s constant and the other gravitational couplings. Full article